(1) Field of the Invention
The present invention relates to active sonar systems, and more specifically to a novel method of processing the Doppler shift from a line array of acoustic sensors to determine the speed of an acoustic wave emitter moving parallel to the line array.
(2) Description of the Prior Art
Certain sonar applications utilize the properties of Doppler effects to analyze the data obtained from acoustic wave receivers. The Doppler effect or Doppler shift expresses the apparent change in the frequency and wavelength of an acoustic wave perceived by an acoustic receiver that is moving relative to the source of the acoustic wave. This relative motion can be caused by the movement of the emitter, the receiver or both the emitter and the receiver. For example, a receiver having velocity νr relative to a source having velocity νs introduces a Doppler shift as follows:
      f    d    =      f    ⁢                            c          +                      v            r                                    c          -                      v            s                              .      
The Doppler shift can be derived for a plane wave from a stationary source having a pressure field of the form p(x,t)=P0ei(ωt-kx). A stationary receiver at x=0 measures the field p(x,0)=P0eiωt, while a receiver moving according to x=−νt, i.e., opposite to the propagation direction of the plane wave, measures the field p(x,t)=P0ei(ω+ων/c)t=P0eiωt(1+ν/c).
The Doppler effect produces a frequency shift when an object emitting acoustic waves is moving relative to an acoustic receiver such as a hydrophone. In the context of a sonar system, the Doppler effect is typically used only to determine the speed of the emitter along the line connecting the emitter and the receiver. When a line array of multiple receivers is used, however, there is the potential for extracting more information about the velocity of the emitter.